Tudor Padurariu

Standard introductory algebra: rings, fields, galois theory.

Calculus III, review of some of calculus I

Mainly methods of integration and the various applications of it (Arc Length, Volume, Area, etc.)

Ring theory, field theory, and Galois theory

I learned more about multivariable calculus. Course took a lot of skills learned in Calc 1 and applied them to more than one variable

The basics of integral calculus including different methods of solving integrals, series and sequences, and differential equations

Rings, Fields, Factorization, Galois Theory

Vectors in 2D and 3D space, coordinate systems, planes, derivatives and integrals of multivariable functions, limits of multivariable functions including L'Hopital and Squeeze theorem, gradients of multivariable functions, optimization of multivariable functions, linear approximation, relative and absolute max/min, space curves.

I learned Calculus II concepts such as integration, types of series and sequences, convergence, divergence, differentials...

I learned about field theory (rings, fields, principal ideal domains, unique factorization domains) and how it connects to group theory through the Galois correspondence. In terms of skills, I learned how to study for mathematics: how to make multiple passes over a large amount of information and distill the big ideas for myself.